Acting, according to Emily Mortimer, is a succession of platonic romances. A "weird flirtation thing" when Andy Garcia played a "sex-obsessed Italian detective" and she was a "nervous little French secretary" in The Pink Panther 2, led to her latest part in City Island. Here, Mortimer plays an aspiring actor who develops an intense friendship with a prison guard and repressed actor who is played, inevitably, by Garcia. "It's a very typical relationship that actors experience all the time," she says, words falling from her mouth in a skittish tumble. "You're put together in very intense circumstances with total strangers, very often from entirely different walks of life, apart from the fact you are both fucked-up actors. It hovers somewhere between romance and friendship. It's a platonic romance.

"It's the speeded-up version of what happens when you start going out with someone." She clicks her fingers. "You tell each other a lot about yourselves very quickly."

It is the things the Italian-American family at the heart of City Island do not tell each other that underpin this indie comedy, which has proved a surprise word-of-mouth hit in America. Mortimer says it is a "really sweet, old-fashioned" movie that has chimed with "unpretentious people who like going to watch a good film." Nobody doesn't like it, even if you're a bit snobby about what you watch."

Not giving anything, including her own career, the hard sell is a trademark for Mortimer. The daughter of the writer, barrister and national treasure John Mortimer, she may have read English and Russian at Oxford, but to her "great shame" never went to drama school and has spent most of her career apologising for it. She has spent the last decade in some memorably self-effacing scenes, including getting spanked and covered in custard in Young Adam and standing naked before her boyfriend in Lovely & Amazing while he listed her physical defects. But she has also moved beyond the "Sloane from the Chilterns" type (as she once put it) she perfected in Woody Allen's Match Point, to play everyone from a detective in Harry Brown to a child killer in Martin Scorsese's Shutter Island.

City Island is a return to more familiar ground; her character, Molly, is exactly the sort of person you might expect to encounter among the frustrated amateurs at acting classes: rather "flighty" and silly but, ultimately, thinks Mortimer, "a good girl". After she and Garcia "got on like a house on fire" on The Pink Panther 2, Garcia suggested she would be perfect to play Molly, but the part had already been taken by another actor. "It was a very clever manipulation," she says, laughing. "I thought, 'Why the fuck have you got someone else doing it? If I'm so perfect for it why didn't you ask me?' Then you start getting interested." When the shooting of City Island was delayed, the original actor could no longer appear and Mortimer snapped up the role.

The film is also based on a premise extremely close to Mortimer's heart. The family in the film all have their secrets – the daughter is a stripper, the teenage son (who has the best Juno-style lines) has a love of larger women – but Garcia's character has the biggest of all: a son that no one knows about.

That touched a nerve with Mortimer: five years before his death in January last year, John Mortimer was revealed to have secretly fathered a son with the actor Wendy Craig before his second marriage and the birth of Emily 38 years ago. Mortimer says she did not think about the parallels until she was actually filming – then she realised she was on familiar territory.

"I guess secrets are part of the fabric of everybody's lives. I mean everybody's lives, and guilt is part of the fabric of everybody's lives," she says. "Normal people, who can be good people but do bad things, are very interesting to me, and people that never get a parking ticket or never do a bad thing in their lives can be really dangerous. Without really thinking about it, I am drawn to material that explores those themes a little bit, but they are quite universal themes. They are probably in everything somewhere."

The words may tumble out, but at times Mortimer, who gave birth to her second child, May, in January, puffs with frustration as she struggles to find the right word. "God, my brain is such a sieve," she says. "I'm still breastfeeding and I can't remember anything. It's impossible to have a conversation. It's really daft to agree to an interview. You spend the whole time saying, 'You know that film, you know the one that had that actor, what'shisname, who was in that other one.'"

While she struggles to remember the name of her next film (it's actually called My Idiot Brother), Mortimer has been treating her new-mum malaise by going to the theatre. Last night she celebrated her husband (and fellow actor) Alessandro Nivola's birthday by seeing Arthur Miller's All My Sons in London. "I feel like I need to jolt my brain into action. When you have babies you don't read, you don't do anything, but if you're willing to part with 150 bucks (£98), you can go to the theatre and make your brain work for a second.

"It is brilliant going to the theatre and being forced to sit and listen and think about life. It can be almost a near-religious experience. I'm sounding really over the top now, but as an atheist who lives in this secular world, you never get to sit on your own and think about things. That is as near as it gets."

Mortimer, on first sight, seems quintessentially English. Her world is full of phrases like "fucking terrifying" and "making heavy weather of things" and "fruity old luvvies". When she is in New York, she says, "someone just has to say the word 'Kennington' and I'll burst into tears." So I am almost disappointed to hear she recently became an American citizen. "I'm quite disappointed in myself," she says. "I'm both though." She became a citizen for "cynical" reasons – so that if anything happened to her husband she would not be hit by a 70% inheritance tax rate. "I had to have blood tests, doctors' visits, show photos of our wedding and memorise 100 questions about the constitution. But there's something quite clever about it. By the end you feel, 'I've made it.'"

I wonder if she went to America to avoid being known as John Mortimer's daughter – "I can't really remember now. I'd have to go to a shrink to find out. I've always been drawn to things to help me escape categorisation" – but she says it was because she fell in love with Nivola, who she met on the set of Kenneth Branagh's film of Love's Labour's Lost. She does not rise to suggestions that Britain is too provincial or too hidebound by class, but she does get tired of how opinionated a nation it has become. "There's all these articles in all the newspapers, not just the crap ones, which are all people's opinions about things. Who fucking cares what serious intelligent people think about Posh Spice or Cheryl Cole? There's something about our fascination with that kind of thing that's cool and funny but the opinions are so aggressive." Nevertheless, she still sees things she loves in Englishness, even when watching Miss World on television. "When Miss England was asked if she would win the title, she went, 'Nah.' She was beautiful and really cool-looking. I thought, 'That's a woman after my own heart.' You could see the interviewer's wires just start to fuse. He turned to Miss America and she went, 'Yeah, I'm really excited and I'd be a wonderful Miss World.' The girl who said 'nah' is just so much more appealing to me."

And acting – is it still something that she is almost embarrassed to call her career? "It depends what day of the week it is. I can look at other actors perform and think, 'This is just the most noble thing to be doing with yourself,' especially in the theatre," she says. Her last bout of theatre acting, in New York in Jez Butterworth's Parlour Song, was so scary that she is full of admiration for those who perform every night. "You just watch and think that's just incredible, that's really a noble thing to be doing. You don't know where your next job is coming from, you're 60 years old, you've been doing this all your life and you've got family to support and this is just what you love and what you believe in," she says. "There are times when you feel like you are part of something that is contributing something in a small way and there is some sort of skill and some sort of daring involved – and then there are some days when you just think, 'What the fuck? I'm too old for this and I've got a degree from a really posh university, I should be doing something much more worthwhile with my education.'"

Is ageing an issue for her, then? Does she feel the pressure to have surgery to help her to conform to Hollywood expectations? "I would love to suddenly look 15 years younger – I don't know who wouldn't – but it fucks with your head a little bit. I couldn't carry it off mentally. Also, you can tell. I think they look worse [with surgery]. Everyone looks the same and you have your insecurity about ageing written on your face. Of course, we're all insecure about ageing, but if you can pretend not to care, it's quite sexy."

Now her elder child is at school, Mortimer says she hopes to spend summers in England with her family and continue acting and writing (her adaptation of Lorna Sage's memoir, Bad Blood, is awaiting funding, and she has written another screenplay with her friend, comic actor Dolly Wells). Before Mortimer's daughter was born, she joked that she was worried the baby would look like her father. Does she? "No," she laughs, wandering off into an account of how her dad's jaw was "such an odd shape" that the Royal School of Dentistry displayed moulds of it in lectures. "It was such a freak jaw. I was living in dread that was going to emerge, but she's gorgeous."

The one nice thing about having children – one of the nice things, she corrects herself – is "all that weird self-effacing neurotic English thing doesn't hold true for my kids. I don't talk them down. I can't believe I don't. You'd think I'd be a prime candidate. In fact, I do the opposite. I bore people with how brilliant they are. Because it doesn't seem like they are connected to you at all. It's like a stork brought them. You realise this the minute they come out. This person is already who they are and they are already brilliant and I've had no impact on it whatsoever."